## Kodai Mathematical Journal

### Holomorphic motions in the parameter space for the relaxed Newton's method.

Hartje Kriete

#### Abstract

It is a well known fact, that for certain polynomials $f$ the relaxed Newton's method $N_{f,h}(z) = z - h\frac{f(z)}{f'(z)}$ associated with $f$ has some extraneous attracting cycles. In the case of cubic polynomials the set of these bad conditioned polynomials has been intensively studied and described by means of quasi--holomorphic surgery and holomorphic motions, cf.~\cite{haeseler:1988}. In the present paper we will generalize this description to polynomials of higher degree.

#### Article information

Source
Kodai Math. J., Volume 25, Number 2 (2002), 89-107.

Dates
First available in Project Euclid: 17 December 2003

https://projecteuclid.org/euclid.kmj/1071674434

Digital Object Identifier
doi:10.2996/kmj/1071674434

Mathematical Reviews number (MathSciNet)
MR2004f:37060

Zentralblatt MATH identifier
1016.37020

#### Citation

Kriete, Hartje. Holomorphic motions in the parameter space for the relaxed Newton's method. Kodai Math. J. 25 (2002), no. 2, 89--107. doi:10.2996/kmj/1071674434. https://projecteuclid.org/euclid.kmj/1071674434